The first book written in America was John A True Relation?

That's not quite right. While John A True Relation (1608) was a significant work, it wasn't the first book written in America.

The honor of the first book goes to A Brief and True Narrative of the Strange and Grevous Accidents by Sea, which Befell the Ship Called The Blessing of London (1602), written by Captain George Waymouth, a captain in the English Navy.

This book chronicled his journey to the New World and his interactions with the Native Americans.

While John A True Relation is known for being the first book printed in English in America, it's important to note that A Brief and True Narrative was written in the New World before any printing press arrived.